Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2022; 59(4): 1019-1044

Published online July 31, 2022 https://doi.org/10.4134/BKMS.b210607

Copyright © The Korean Mathematical Society.

Approximate projection algorithms for solving equilibrium and multivalued variational inequality problems in Hilbert space

Nguyen Minh Khoa, Tran Van Thang

Electric Power University; Electric Power University

Abstract

In this paper, we propose new algorithms for solving equilibrium and multivalued variational inequality problems in a real Hilbert space. The first algorithm for equilibrium problems uses only one approximate projection at each iteration to generate an iteration sequence converging strongly to a solution of the problem underlining the bifunction is pseudomonotone. On the basis of the proposed algorithm for the equilibrium problems, we introduce a new algorithm for solving multivalued variational inequality problems. Some fundamental experiments are given to illustrate our algorithms as well as to compare them with other algorithms.

Keywords: Equilibrium problem, multivalued variational inequality problem, subgradient, approximate projection, pseudomonotone, Tseng's extragradient method

MSC numbers: 65K10, 90C25, 47J25, 47J20, 91B50

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